The present invention relates to a new and distinct strawberry variety named ‘BG-4.367’. This new variety is a result of a controlled cross made in 2004 in an ongoing breeding program between strawberry variety designated ‘BG-633’ (U.S. Plant Pat. No. 13,320) and strawberry variety designated ‘BG-414.065’ (a non-patented selection). Due to the combining of the reciprocal seed lots, it is unknown as to which parent variety is the seed parent and which parent variety is the pollen parent. The variety is botanically known as Fragaria ananassa. 
The seedling resulting from the aforementioned cross was selected from a controlled breeding plot in Ventura County, Calif. in the winter of 2006. After its selection, the new variety was asexually propagated by stolons in both Siskiyou County, Calif. and San Joaquin County, Calif. The new variety was extensively tested over the next several years in fruiting fields in Ventura County, Calif. This propagation has demonstrated that the combination of traits disclosed herein as characterizing the new variety are fixed and remain true to type through successive generations of asexual reproduction.